Question

One of the factor of
(x+2y)^2-8 x y
​

Answer 1

Answer:$(x-2y)^{2}$

Step-by-step explanation:

We know that, $(a+b)^{2}-4ab=(a-b)^{2}$

$(a+b)^{2}-4ab=a^{2}+2ab+ b^{2}-4ab=a^{2}-2ab+ b^{2}=(a-b)^{2}$

here,

$(x+2y)^{2}-8xy$

=$(x-2y)^{2}$

Answer 2

Answer:

(x-2y)

Step-by-step explanation:

for doing factorization,

first solve the equation

(x+2y)^2 - 8xy

= x^2 + 4y^2 + 4xy- 8xy As we Know, ( a+b)^2 = (a^2 + b^2 - 2ab)

= x^2 + 4y^2 - 4xy

which can be written in the form

(a^2 + b^2 - 2ab) = ( a-b)^2

therefore

x^2 + 4y^2 - 4xy can be written as

(x-2y)^2

hence the factors of the given equation are

(x-2y) and (x-2y)